1. Create two layers based on the same Counties feature class. I will call them Layer 1 and Layer 2 to keep it straight.
2. Select your County of interest in Layer 1. Use the Create New Selection option is Select By Attributes or get a user selection.
3. On Layer 1 Select By Location on itself (Layer 1) and apply the Intersect option without any buffer or a very small positive buffer (say 1 foot) and select against itself. This will be the selection of the County itself plus every County that adjoins the original County. Use the Create New Selection option.
4. Select by Location against Layer 2 using the Layer 1 feature selection as the location to base the search on and apply the Intersect option without any buffer or a very small positive buffer (say 1 foot). Use the Create New Selection option. This will be the selection of every County that is out as far as 2 Counties away from the original County including all Counties within that boundary.
5. Select by Location against Layer 2 using the Layer 1 feature selection as the location to base the search on and apply a -1 foot (or very small negative) buffer to the selection. Use the Remove From Selection option. This will remove all Counties that included the County itself and the first ring of Counties surrounding it (Layer 1 Selection). Layer 2 now contains every County that is 2 Counties away from the original and only those Counties.
6. To transfer the selection of Layer 2 back to Layer 1 use Layer 2 as the feature selection you want to select against Layer 1 and apply a -1 (or very small negative) buffer to the Layer 2 feature selection. Use the Create New Selection option.
No new features had to be created. This assumes your County layer is topologically correct and that no gaps or overlaps exist along any shared border between any two Counties.
This can be done with real layers in a map or with inmemory layers, so Layer 1 could be a real map layer and Layer 2 could be an inmemory layer if you don't want it to actually appear in your map, and by using step 6 the final result will appear in Layer 1 in your map.
These are the steps you would have to follow to do this manually in Desktop to achieve the effect you want (except that in Desktop there would not be any inmemory layer and you would have to have 2 real layers that were based on the same feature class in your map).
